4

Q1. If four sides of a quadrilateral are of length 4 cm, 5 cm, 4.9 cm and 5.3 cm and one of its diagonal is equal to one of its sides, then the length of that diagonal is

• 4.9 cm
• 5.3 cm
• 4 cm
• 5 cm

Solution

The diagonal is either greater than all the sides or equal to the largest side. So, the length of the diagonal of the quadrilateral is 5.3 cm.

Q2. The quadrilateral formed by joining the mid-points of the sides of a quadrilateral ABCD taken in order is a square only if

• Diagonals of ABCD are equal
• Diagonals of ABCD are equal and perpendicular
• Diagonals of ABCD are perpendicular
• None of these

Solution

A square has equal and perpendicular diagonals.

Q3. What is the sum of angles of quadrilaterals?

• 90°
• 180°
• 270°
• 360°

Solution

The sum of angles of a quadrilateral is 360^o. 

Q4. A quadrilateral with adjacent sides not equal but with angles measuring 90˚ is known as a 

• Rhombus
• Rectangle
• Square
• Parallelogram

Solution

Adjacent sides of a rectangle are not equal, but its angles measure 90˚. 

Q5. The following elements are sufficient to construct a quadrilateral:

• 4 sides and 1 angle
• 3 sides and 1 angle
• 2 sides and 1 angle
• 1 side and 1 angle

Solution

Provided 4 sides and 1 angle, a quadrilateral can be constructed.

Q6. To construct a parallelogram with sides 4 cm and 5 cm, the minimum requirement is that of the measurement of ______ angle/s.

• One
• Two
• Three
• Four

Solution

If two sides of a parallelogram are known, only one angle is required for its construction.

Q7. When the opposite sides are equal and all the angles are right angles, the quadrilateral is a 

• Parallelogram
• Trapezium
• Rectangle
• Kite

Solution

When the opposite sides are equal and all the angles are right angles, the quadrilateral is a rectangle.

Q8. A rectangle whose adjacent sides are equal is a

• Square
• Rhombus
• kite
• Trapezium

Solution

All sides of a sure are equal.

Q9. The quadrilateral that can be constructed with the minimum number of measurements is a 

• Square
• Rhombus
• Parallelogram
• Rectangle

Solution

Since all sides of a square are equal and each angle is a right angle, a square can be constructed provided the measure of its side only.

Q10. In a rhombus with diagonal 10 cm, each side will be ______ 5 cm.

• Greater than
• Smaller than
• Equal to
• Smaller than or equal to

Solution

Q11. Given the length of two diagonals of a parallelogram, we need measurement  of at least

• one side
• two sides
• three sides
• four sides

Solution

If the measurement of two diagonals and a side is given, we can construct a parallelogram.

Q12. A parallelogram can be constructed uniquely if

• the measurement of two adjacent sides and a diagonal is given
• the measurement of one angle is given
• measurement of one side is given
• measurement of two diagonals is given

Solution

A parallelogram can be uniquely constructed if its two adjacent sides and a diagonal are given.

Q13. A quadrilateral is a square if and only if it is a 

• Rhombus
• Rectangle
• Rhombus and a Rectangle
• Kite

Solution

Since all the sides of a square are equal, so it is a rhombus and each angle of a square is a right angle, hence it is a rectangle. Thus, a quadrilateral is a square if and only if it is a Rhombus and a Rectangle.

Q14. If EFGH is a parallelogram, then

• EF is parallel to EG
• EF is parallel to GH
• GH is parallel to HA
• EF is parallel to FG

Solution

If EFGH is a parallelogram, then EF is parallel to GH. 

Q15. We can construct a parallelogram with

• 2 sides
• 1 angle
• 1 side and 1 diagonal
• 2 sides and 1 diagonal

Solution

A parallelogram can be constructed uniquely if the measurement of its two sides (opposite sides are equal) and a diagonal are given.

Q16. To construct a quadrilateral, given the measures of three of its sides, we also need to know the measure of

• 1 diagonal
• 2 included angles
• Fourth side
• 1 angle

Solution

A quadrilateral can be constructed uniquely if the measures of three sides and two included angles are given.

Q17. A quadrilateral can be constructed uniquely if the length of its _______ sides and a diagonal is given.

• Four
• Three
• One
• Two

Solution

A quadrilateral can be constructed uniquely if the length of its four sides and a diagonal is given.

Q18. If ABCD is a parallelogram then

• AB is parallel to BC
• AB is parallel to AC
• AB is parallel to CD
• CD is parallel to DA

Solution

For a parallelogram ABCD, AB is parallel to CD.

Q19. Which of the following measurements are necessarily needed to construct a parallelogram uniquely?

• Two sides and one diagonal
• One side and one diagonal
• Two sides
• Two diagonals

Solution

A parallelogram can be constructed uniquely if the measurement of one diagonal and two sides are given.

Q20. A kite can be constructed with

• 1 diagonal and a pair of equal sides
• 2 diagonals
• 2 adjacent angle and 2 non equal sides
• A pair of equal sides and equal angles

Solution

A kite can be constructed if the measurement of two non-equal sides and two adjacent angles are given.

Q21. A rectangle whose adjacent sides are equal is a

• Kite
• Square
• Rhombus
• Trapezium

Solution

A rectangle whose adjacent sides are equal is a square. 

Q22. For construction of a rhombus, we need the measures of 

• One side
• Two sides
• One diagonal
• Two diagonals

Solution

For construction of a rhombus, we need the measures of two diagonals. 

Q23. A student wants to construct a quadrilateral ABCD with the measurements AB = 3 cm, BC = 4 cm, CD = 4.5 cm, AD = 2 cm and BD = 6 cm but he could not construct it. What could be the reason?

• In ΔABD, sum of sides AB and AD is less than the third side BD
• Length of a diagonal can not be less than the length of the sides of the quadrilateral
• A quadrilateral cannot be constructed if the measurements of four sides and a diagonal is given
• In ΔBCD, sum of the sides BC and CD is greater than the third side BD

Solution

In a triangle, sum of the length of any two sides should always be greater than the length of the third side. Here, sum of the length of sides AB and AD is less than the length of the third side BD of triangle ABD. Hence, the quadrilateral cannot be constructed.

Q24. Construct a quadrilateral LMNO where LM = 8cm, MN = 9cm, NO=10 cm and ∠M=115° and ∠N=80°. Arrange the following in the proper order   i. Join L, M, N, O.  ii. Draw an angle of 105° at M and 80° at N.  iii. Locate L and O. iv. Draw MN.

• i-iii-iv-ii
• iii-ii-i-iv
• iv-ii-iii-i
• i-ii-iv-iii

Solution

The correct order is Draw MN. Draw an angle of 105° at M and 80° at N. Locate L and O. Join L, M, N, O. 

Q25. In a rhombus with diagonal 8 cm, each side will be ____ 4 cm.

• Equal to
• Smaller than
• Greater than
• Smaller than or equal toc

Solution

In a rhombus with diagonal 8 cm, each side will be greater than 4 cm. 

Q26. A parallelogram can be constructed if

• One side and one angle are given
• One pair of opposite sides and an angle are given
• Two adjacent sides and one angle are given
• One side and two angles are given

Solution

A parallelogram can be constructed provided its two adjacent sides and one angle.

Q27. If a diagonal AC of a parallelogram ABCD is of length 6 cm and side AB is of length 4 cm, then the length of side BC will be

• = 2 cm
• < 2 cm
• > 2 cm
• < 1 cm

Solution

We know that sum of any two sides of a triangle is greater than its third side. In a parallelogram ABCD, consider the triangle ABC. We have, AB + BC > AC BC > 6 cm - 4 cm BC > 2  cm

Q28. A quadrilateral with four congruent sides and four congruent angles is

• Rectangle
• Square
• Rhombus
• Trapezium

Solution

A quadrilateral with four congruent sides and four congruent angles is a square.

Q29. Only ________ element(s) is/are enough to construct a rhombus.

• One
• Two
• Three
• Four

Solution

Two elements are enough to construct a rhombus.

Q30. A quadrilateral whose opposite sides and all the angles are equal is a 

• Rectangle
• Rhombus
• Trapezium
• parallelogram

Solution

The opposite sides and all the angles are equal in a rectangle.

Q31. The minimum number of measurements required to construct a square is

• Four
• Three
• Two
• One

Solution

We can construct a square if the length of one of its sides or diagonals is known. 

Q32. Which of the following is not a property of parallelogram?

• Opposite sides are equal
• Opposite angles are equal
• Diagonals are equal
• Diagonals bisect each other

Solution

In a parallelogram, diagonals are not equal.

Q33. A quadrilateral, in addition to the conditions sufficient for its construction, must also satisfy: (i) Triangle inequality property (ii) Angle sum property of a quadrilateral Which of the above statements is/are true?

• Both
• (i) only
• (ii) only
• None

Solution

A quadrilateral, in addition to the conditions sufficient for its construction, must satisfy both the statements below. (i) Triangle inequality property (ii) Angle sum property of a quadrilateral

Q34. A rectangle WXYZ can be constructed if the length of

• WX and WZ are given
• XY is given
• WX and ZY are given
• YZ is given

Solution

A rectangle can be constructed given the length of its adjacent sides. Hence, a rectangle WXYZ can be constructed if the length of WX and WZ are given.

Q35. For which of the following quadrilaterals, are the diagonals equal? 

• Rectangle
• Rhombus
• Kite
• Trapezium

Solution

The diagonals of a rectangle are equal.

Q36. The minimum number of measurements required to construct a rectangle are  

• one
• two
• three
• four

Solution

The minimum number of measurements required to construct a rectangle are two.

Q37. To construct a quadrilateral uniquely, it is necessary to know 

• 3 measurements
• 4 measurements
• 5 measurements
• 2 measurements

Solution

To construct a quadrilateral uniquely, it is necessary to know 5 measurements. Also, we will need to know a combination of specific 5 measurements.

Q38. ______ measurements can determine a quadrilateral uniquely.

• Four
• Five
• Three
• Six

Solution

Five measurements can determine a quadrilateral uniquely.

Q39. What is the maximum number of obtuse angles that a quadrilateral can have?

• 1
• 2
• 3
• 4

Solution

The maximum number of obtuse angles that a quadrilateral can have is 3

Q40. A special kind of ………… is called a parallelogram. 

• Triangle
• Circle
• Line
• Polygon